DIVERGENCE AND DIFFLUENCE ARE NOT SYNONYMS
Eric R. Thaler
National Weather Service Forecast Office
Denver, Colorado
1. Introduction
often even a qualitative) assessment of the divergence using
streamline,s and isotachs is next to impossible.
Instead of using streamlines and isotachs , many forecasters
use geopotential height charts to infer horizontal velocity
divergence . To do this, they look for areas where the geopotential height lines spread out looking downstream. These
areas are labeled "diffluent flow ," and it is incorrectly
assumed that horizontal divergence is automatically occurring there. In these cases little attention is given to the stretching term in (1).
What makes this method suspect is that when forecasters
use geopotential heights to deduce the wind vectors they are
often assuming that the flow is geostrophic. Thus , where
geopotential height contours spread out (diffluent geostrophic
flow) there must be, by definition, geostrophic speed convergence. Hence the stretching term in (I) is negative and the
spreading term is positive. Which has the greater magnitude?
It's anybody's guess. Furthermore, assuming a constant
Coriolis parameter, the geostrophic wind is nondivergent!
So any use of the geostrophic wind to determine horizontal
velocity divergence is not theoretically sound.
A glaring example showing how diffluent flow is not necessarily divergent is depicted in Figure I. Shown are the NOM
geopotential heights and divergence at 500 mb created using
gridded model output. Note how the geopotential height lines
("geostrophic streamlines") spread out over the area extending from eastern Nebraska to western Tennessee. This is the
region of diffluent flow. The dashed lines in this same area
are isopleths of the horizontal divergence of the actual wind.
Note that the values are negative which means that horizontal
convergence is occurring here!
One of the main tasks operational meteorologists face in
day to day forecasting is determining the sign of the vertical
velocity. In situations where the dynamic forcing for vertical
motion is weak, forecasters often attempt to determine this
parameter through a kinematic approach (Holton 1979). This
method requires knowledge of the horizontal velocity divergence.
Until the advent of advanced datasets, forecasters have not
had the tools necessary to quickly obtain an accurate assessment of the horizontal velocity divergence. The diagnosis of
diffluence has , on the other hand, been quite easy. Consequently, diffluence and horizontal velocity divergence are often
considered to be the same thing, with areas of diffluent flow
assumed to be divergent as well. Diffluence does NOT automatically imply divergence and making that assumption can lead to
incorrect estimates of the implied vertical motion.
2. Discussion
Although the concepts of divergence and diffluence have
existed for a long time (e.g., Petterssen 1956), confusion still
remains in the application of these ideas in the operational
setting. To see how horizontal velocity divergence and diffluence differ, it is helpful to use the natural coordinate system. In two dimensions, this is an orthogonal coordinate
system with the s-axis parallel to the flow at each point (positive downstream) and the n-axis perpendicular to it with positive values to the right of the flow looking downstream. Following Saucier (1955), with V representing the magnitude of
the velocity vector (wind speed) and a the wind direction in
radians (degrees x 1T/180), the horizontal velocity divergence
can be written as
.
Divergence
av
= -
as
aa
+ V-a
n
Acknowledgments
Many thanks to Drs. Charles Doswell and James Moore for
their helpful suggestions and comments and to Steven Weiss
for his assistance.
(1)
The first term in (I) is called the stretching (or speed divergence) term and describes how the wind speed is changing
along the s-axis (streamline) . If the wind speed is increasing
downstream then this term is positive (also known as speed
divergence). The second term in (I) is the spreading (or the
directional divergence) term and describes how the wind
direction is changing along the n-axis (perpendicular to the
flow) . If the flow spreads out downstream (diffluence), then
this term is positive (V is always greater than zero).
From (1) it is obvious that diffluence is only a part of the
total horizontal divergence. In evaluating horizontal velocity
divergence, one must consider not only the pattern of the
streamlines but also the structure of the wind speed along
the streamlines. What makes the evaluation difficult is that
oftentimes the two terms in (1) oppose each other, that is, in
areas where the streamlines spread out downstream the wind
speed decreases. Consequently, an accurate quantitative (and
Author
Eric Thaler is the Science and Operations Officer at the
National Weather Service Forecast Office in Denver, Colorado, a position he has held since September of 1990. Prior to
that he held forecaster positions at National Weather Service
stations in Denver and Medford, Oregon, and training positions at Fairbanks , Alaska and Albuquerque, New Mexico .
He received the Bachelor of Science degree in meteorology
from the University of Utah in 1982 where he was also elected
a member of Phi Beta Kappa. He received the Master of
Science degree in mathematics from the Colorado School of
Mines in 1989. His primary interests include synoptic and
dynamic meteorology and the integration of new technologies, datasets, and numerical models into the operational forecasting environment.
28
Volume 17 Number 1 February, 1992
29
Fig. 1. NGM geopotential height (thick lines, gpm) and isopleths of divergence (thin lines, *10- 5
sec - 1). Dashed thin lines denote negative divergence or convergence.
References
Holton, J. , 1979: An Introdu ction to Dynamic Meteorology, 2nd
Ed. Academic Press, 391 pp.
Petterssen, S., 1956: Weather Analysis and Forecasting, Vol. I.
McGraw Hill , 428 pp.
Saucier, w. J., 1955: Principles of Meteorological Analysis.
Univ. of Chicago Press, 438 pp.
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